Lady Gaga calls her legion of online followers Little Monsters, Nicki Minaj her Barbz, Jessie J her Heartbeats, but I want to be in Scottish singer Nina Nesbitt's gang most of all — they're called Nesbians.

There are lots of them too, considering the 18-year-old is still a fledgling musician who reached the charts for the first time only this month. She has 80,000 Twitter followers, 66,000 Facebook fans and 1.5 million YouTube views for the current single, Stay Out. The skyscraping statistics of the digital pop world seem to mean more to her than a traditional chart placing, though she admits to being annoyed at getting bumped just out of the top 20 by the late arrival of Ding Dong! The Witch Is Dead.

“If people really like your music but you’re not selling so many records, I don’t think it really matters,” she tells me over the breadbasket in a central London brasserie. “If it gets people turning up to your shows I don’t think it’s too much of an issue.”

And turn up they do, making Nesbitt’s habit of coming out to chat to fans after her gigs increasingly problematic. “It’s started to get really out of hand, all these 14-year-old girls shoving each other. When I came out in Edinburgh a little while ago the whole street was covered in people, blocking the cars. It’s got really dangerous.”

She shrugs, musses her already mussed peroxide mane and fiddles with the bracelets on her left wrist — about a dozen of them, one saying her own name, one saying “Hannah”. Fans give them to her and then look out for them when she’s on TV or in another of her YouTube videos. They used to go halfway up her arm but she had to cut some off.

She says she has plenty of fans who are older now too, and a fair few “lads”. They give her their numbers but she wouldn’t dream of calling. But mainly it’s teenage girls, who see themselves in this tall, skinny girl, not long out of school, with her bright red lips and violent slashes of black eye make-up. Their interest is unexpected, since theirs is the demographic least likely to go for her brand of fairly conventional acoustic pop, with similar energy and melody to her fellow Scots and Radio 2 favourites KT Tunstall and Amy MacDonald. But like Taylor Swift or Ed Sheeran, with their lyrics about carefree youth and frequent heartbreak, she’s much more tuned into the thoughts and fears of teens today.

The cheery strum of Stay Out teases the cool boys. “Chequered shirts and chino trousers/Is this some kind of uniform?/It seems that they think they’re gangsters/They’ve barely started sixth form,” she sings in a soft but powerful voice. The subtler electronic groove No Interest describes a quieter night spent trying to avoid an old flame: “Get a text from Claire and a Rachel/Telling me that my ex tried to kiss them/Last night we were at Revolution/Had enough so I went to get some chips.” She mentions a new song, 18 Candles, all about growing up, which she thinks will become her first big hit this summer.

She found a ready-formed fanbase thanks to the enthusiasm of Sheeran, whom she approached and asked for advice in 2011 after he appeared on a Scottish radio show. He gave her his guitar and asked her to sing him a song right there. She did one of her first compositions, Standing on One Leg, and he was impressed enough to invite her on tour. She also appeared as an ex-girlfriend in the video for his single, Drunk.

She rolls her eyes when I bring him up, complaining that she gets asked about him in every interview. It frustrates her because the question is usually about whether they are a couple. “It’s really annoying, that people would only think I was playing with him because we were going out. We’re not. I don’t understand why people would be interested in that kind of thing. I wish they’d just listen to the music.”

But pop life today is about much more than the music, and Nesbitt’s approach is a prime example. She’s constantly communicating with her fans on social media and giving them video diaries detailing her progress on her debut album, due in early autumn after two more singles. It’s being produced and co-written by Jake Gosling, best known for his work with Sheeran and One Direction, in his Sunningdale studio.

Like Justin Bieber and Conor Maynard, she started out posting videos of herself singing cover versions on YouTube. Beginning at 14, it took two years for her to start seeing serious viewer numbers but it earned her interest from management companies before she had ever played a gig. “I couldn’t get gigs because you need to be 18 in most venues,” she says. “So I started doing videos. I wasn’t thinking about getting a record deal, I just wanted to know if people thought I was good.”

The first song she attempted was Kelly Clarkson’s Already Gone, which she has now taken down out of embarrassment. A school friend who wanted to be a film-maker started making the videos with her for £20 a time. She eventually found that you get more attention if you do something currently in the charts (as more people will be searching for it) and if you get out of your bedroom. She did one in a forest and one on a lake. Then she started sharing the videos of other singer-songwriters doing the same thing, such as Gabrielle Aplin (of John Lewis ad fame), and they started helping her back.

She understands more than most the need to keep herself out there to make it in pop but in conversation she turns out to be quite a private person. An only child raised in a village just outside Edinburgh, she doesn’t especially want to talk about her parents — Mum is a Swedish social worker, Dad a manager in the defence industry — though she says they’ve been encouraging. They’ve seen her in the public eye since she was in shop windows of the Quiz clothing chain, modelling their “back to school” range at 15.

“I only ever want to put music out there,” she insists. “I never want people to know who I’m going out with or about my family. But it’s difficult, because when people have seen you online since you were 14, they feel like they know you.”

Currently living near her producer in Surbiton while she finishes her album, she tries to keep things as normal as possible, visiting her old friends in their various university halls when she can. “I still get the bus into town, still do all the things I used to before I was signed.”

It has to be this way, otherwise what would this chronicler of teenage life have to sing about? But if this year goes according to plan, her bus is going to have to battle through an increasing number of those Nesbian roadblocks.

Stay Out is out now on Universal. Tickets go on sale today for June 13, The Barfly, NW1 (020 7961 4244, barflyclub.com)